%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET916+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Apr 9 08:39:35 PM UTC 2025
% Result : Theorem 59.24s 42.71s
% Output : CNFRefutation 59.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 24 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 49 ( 16 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 41 ( 16 ~; 15 |; 6 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 40 ( 39 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ in > disjoint > empty > unordered_pair > set_intersection2 > #nlpp > #skF_1 > #skF_4 > #skF_10 > #skF_5 > #skF_6 > #skF_2 > #skF_9 > #skF_8 > #skF_3 > #skF_7
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_1',type,
'#skF_1': ( $i * $i * $i ) > $i ).
tff(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i * $i ) > $i ).
tff('#skF_10',type,
'#skF_10': $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_5',type,
'#skF_5': $i ).
tff('#skF_6',type,
'#skF_6': $i ).
tff(set_intersection2,type,
set_intersection2: ( $i * $i ) > $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i * $i ) > $i ).
tff(empty,type,
empty: $i > $o ).
tff(disjoint,type,
disjoint: ( $i * $i ) > $o ).
tff('#skF_9',type,
'#skF_9': $i ).
tff('#skF_8',type,
'#skF_8': $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i * $i ) > $i ).
tff('#skF_7',type,
'#skF_7': ( $i * $i ) > $i ).
tff(f_89,negated_conjecture,
~ ! [A,B,C] :
~ ( ~ in(A,B)
& ~ in(C,B)
& ~ disjoint(unordered_pair(A,C),B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_zfmisc_1) ).
tff(f_78,axiom,
! [A,B] :
( ~ ( ~ disjoint(A,B)
& ! [C] : ~ in(C,set_intersection2(A,B)) )
& ~ ( ? [C] : in(C,set_intersection2(A,B))
& disjoint(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_xboole_0) ).
tff(f_53,axiom,
! [A,B,C] :
( ( C = set_intersection2(A,B) )
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
& in(D,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
tff(f_33,axiom,
! [A,B] : ( unordered_pair(A,B) = unordered_pair(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
tff(f_44,axiom,
! [A,B,C] :
( ( C = unordered_pair(A,B) )
<=> ! [D] :
( in(D,C)
<=> ( ( D = A )
| ( D = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
tff(c_56,plain,
~ disjoint(unordered_pair('#skF_8','#skF_10'),'#skF_9'),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_60,plain,
~ in('#skF_8','#skF_9'),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_58,plain,
~ in('#skF_10','#skF_9'),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_234,plain,
! [A_62,B_63] :
( in('#skF_7'(A_62,B_63),set_intersection2(A_62,B_63))
| disjoint(A_62,B_63) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_30,plain,
! [D_18,A_13,B_14] :
( in(D_18,A_13)
| ~ in(D_18,set_intersection2(A_13,B_14)) ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_260,plain,
! [A_62,B_63] :
( in('#skF_7'(A_62,B_63),A_62)
| disjoint(A_62,B_63) ),
inference(resolution,[status(thm)],[c_234,c_30]) ).
tff(c_4,plain,
! [B_4,A_3] : ( unordered_pair(B_4,A_3) = unordered_pair(A_3,B_4) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_206,plain,
! [D_54,B_55,A_56] :
( ( D_54 = B_55 )
| ( D_54 = A_56 )
| ~ in(D_54,unordered_pair(A_56,B_55)) ),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_552,plain,
! [D_106,A_107,B_108] :
( ( D_106 = A_107 )
| ( D_106 = B_108 )
| ~ in(D_106,unordered_pair(A_107,B_108)) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_206]) ).
tff(c_246294,plain,
! [A_51955,B_51956,B_51957] :
( ( '#skF_7'(unordered_pair(A_51955,B_51956),B_51957) = A_51955 )
| ( '#skF_7'(unordered_pair(A_51955,B_51956),B_51957) = B_51956 )
| disjoint(unordered_pair(A_51955,B_51956),B_51957) ),
inference(resolution,[status(thm)],[c_260,c_552]) ).
tff(c_247004,plain,
( ( '#skF_7'(unordered_pair('#skF_8','#skF_10'),'#skF_9') = '#skF_8' )
| ( '#skF_7'(unordered_pair('#skF_8','#skF_10'),'#skF_9') = '#skF_10' ) ),
inference(resolution,[status(thm)],[c_246294,c_56]) ).
tff(c_247005,plain,
'#skF_7'(unordered_pair('#skF_8','#skF_10'),'#skF_9') = '#skF_10',
inference(splitLeft,[status(thm)],[c_247004]) ).
tff(c_28,plain,
! [D_18,B_14,A_13] :
( in(D_18,B_14)
| ~ in(D_18,set_intersection2(A_13,B_14)) ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_261,plain,
! [A_62,B_63] :
( in('#skF_7'(A_62,B_63),B_63)
| disjoint(A_62,B_63) ),
inference(resolution,[status(thm)],[c_234,c_28]) ).
tff(c_247024,plain,
( in('#skF_10','#skF_9')
| disjoint(unordered_pair('#skF_8','#skF_10'),'#skF_9') ),
inference(superposition,[status(thm),theory(equality)],[c_247005,c_261]) ).
tff(c_247218,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_56,c_58,c_247024]) ).
tff(c_247219,plain,
'#skF_7'(unordered_pair('#skF_8','#skF_10'),'#skF_9') = '#skF_8',
inference(splitRight,[status(thm)],[c_247004]) ).
tff(c_247239,plain,
( in('#skF_8','#skF_9')
| disjoint(unordered_pair('#skF_8','#skF_10'),'#skF_9') ),
inference(superposition,[status(thm),theory(equality)],[c_247219,c_261]) ).
tff(c_247433,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_56,c_60,c_247239]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET916+1 : TPTP v9.0.0. Released v3.2.0.
% 0.07/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.12/0.34 % Computer : n020.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Apr 8 21:50:19 EDT 2025
% 0.12/0.34 % CPUTime :
% 59.24/42.71 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 59.24/42.72
% 59.24/42.72 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------